After every major assassination in the series, there is always a dialogue between the assassin and the target. Why does it always take place in this "animus void"? Is everyone, including guards, just standing around while the assassin talks to his victim? This always bothered me.

I understand it as you had that conversation at some point, but you're not doing exactly what the ancestor did so they replay this convo in animus void. Or maybe Assassins have freeze time ability they don't brag about. Those damn TWCB, who knows what sorcery they hide!

I don't think there's a good in-universe "flavor" explanation for it - I just took it as an interesting surrealist aesthetic choice by the devs in AC1. It was neat in the earlier games, where there were more times that an assassination was stealthy and could happen one-on-one.

I'm not sure that it has aged very well as the franchise has evolved, though.